Why Does Trend Growth Affect Equilibrium Employment? A New Explanation of an Old Puzzle Michael W. L. Elsby

Matthew D. Shapiro

University of Edinburgh and NBER

University of Michigan and NBER

May 2, 2011

Abstract That the employment rate appears to respond to changes in trend growth is an enduring macroeconomic puzzle. This paper shows that, in the presence of a return to experience, a slowdown in productivity growth raises reservation wages, thereby lowering aggregate employment. The paper develops new evidence that shows this mechanism is important for explaining the growth-employment puzzle. The combined e¤ects of changes in aggregate wage growth and returns to experience account for all the increase from 1968 to 2006 in nonemployment among low-skilled men and for approximately half the increase in nonemployment among all men.

We would like to thank anonymous referees, John Bound, Charles Brown, Damon Clark, Robert Hall, Christopher House, Miles Kimball, Patrick Kline, David Romer, Gary Solon, and Sarah Turner for helpful comments, Chinhui Juhn and Lance Lochner for sharing their data at the early stages of this project, and David Ratner for excellent research assistance. We also thank participants in seminars at the Einaudi Institute for Economics and Finance, Stanford, Berkeley, the New York Fed, the Hebrew University, Tel Aviv, Michigan State, Edinburgh, Ohio State, Toronto, Michigan, Warwick, Florida, the NBER Labor Studies Summer Institute, and Western Ontario. This paper was previously circulated as “Stepping O¤ the Wage Escalator: The E¤ects of Wage Growth on Equilibrium Employment.”

I

Introduction

Explaining the variation in rates of employment over time has been a central question for labor and macroeconomics and for public policy for several decades. The sudden and sustained increase in nonemployment beginning in the early 1970s occurred at the same time as the rate of growth of productivity and wages slowed. From 1970 to 1980, the nonemployment rate of prime age adult males in the United States rose from 6 percent to 12 percent (see Figure 1A). These trends were associated with dramatic declines in labor market attachment among the low-skilled. For high school dropouts, rates of nonemployment rose from 10 percent to 23 percent over the same period (Figure 1B). The 1970s also saw a dramatic slowing of the rate of productivity and wage growth. Trend growth in wages for all adult males fell 5 percentage points over the 1970s (Figure 2). Economists have long been tempted to relate the decline in economy-wide wage growth associated with the productivity slowdown of the 1970s to the persistent deterioration in equilibrium employment beginning in the early to mid-1970s.1 Super…cially, the case for a link between productivity growth and employment rates appears simple: Should it be surprising that employment declines when the returns to work have fallen? The theoretical link between productivity growth and equilibrium employment, however, has proved elusive. In traditional models of the aggregate labor market (Layard, Nickell and Jackman, 1991), changes in trend rates of growth of productivity and wages do not a¤ect the steady-state rate of employment. That is, changes in productivity growth a¤ect equally the returns to work and the returns to not working, as any violation of this relation will cause an economy to converge either to full employment or zero employment in the long run. Indeed, in his survey of traditional models of employment determination, Blanchard (2007) concludes that they “deliver, to a …rst order, long run neutrality of unemployment to productivity growth.” Shimer (2010) demonstrates that the same neutrality result arises in a balanced-growth version of the Mortensen and Pissarides (1994) model. While existing theories have clearer implications for the short to medium run link between productivity growth and the rate of employment, the understanding of the link between them in the long run is weaker. To quote Blanchard (2007, p.416), “The truth is we do not know. And this is a serious hole in knowledge.” Existing literature has attempted to break this employment/growth neutrality result. Theoretical work on unemployment in labor markets with frictions has identi…ed two channels through which growth can a¤ect unemployment in the long run. If technological change 1

A prominent early example is Bruno and Sachs (1985). More recently, see Staiger, Stock, and Watson (2001).

1

is embodied in new jobs, a process of creative destruction arises whereby old jobs must be destroyed to update to the technological frontier (Aghion and Howitt, 1994). In this environment, faster growth implies higher rates of obsolescence, increased job destruction and increased unemployment, in contrast to the trends observed in the data. If new technologies are incorporated into all jobs, however, a capitalization e¤ect can occur: If the costs of job creation are borne upfront, higher expected productivity growth causes future pro…ts to be discounted at a lower rate, stimulating …rms’ demand for labor through job creation, and reducing unemployment (Mortensen and Pissarides, 1998; Pissarides and Vallanti, 2007). This paper identi…es a novel and complementary explanation for the longstanding puzzle of providing a theoretical explanation for the observed low-frequency comovement of productivity growth and the employment rate. Our explanation of the puzzle is motivated by an additional salient feature of the data: that the decline in male employment rates was accompanied by sustained declines in labor force attachment. Accordingly, our explanation highlights the role of wage growth in the decision of workers to supply labor. We begin by showing that Blanchard’s neutrality puzzle, which refers to the unemployment margin, applies with the same force to the labor supply margin. Absent the e¤ects we emphasize, standard models of the work/nonwork decision imply that labor supply is unaffected by changes in trend productivity growth. We show that this result is overturned once one recognizes that workers face substantial returns to labor market experience. Since Weiss (1972), it has been well-understood that the joint processes of the accumulation of labor market experience and the decision to supply labor are naturally intertwined. In order to accumulate experience, an individual must work. Consequently, changes in the experienceearnings pro…le that workers face a¤ect the decision of a marginal worker to seek lifetime employment. A novel and important outcome of our theoretical analysis, however, is that this interplay between the return to experience and labor supply also interacts with trend growth in wages in determining whether or not an individual chooses to work. Faster growth in aggregate wages compounds the return to experience, raising equilibrium employment. The interaction between these two processes in the model generates a strong theoretical rationale for a connection between rates of wage growth and the level of equilibrium employment. Intuitively, if the “wage escalator”‡attens, either from a decline in the return to experience or from a slowdown in productivity growth, the payo¤ to being engaged in the workforce over a lifetime falls, and a marginal worker will …nd employment a less attractive prospect. To examine the extent to which this new explanation can provide an account of long-run trends in measures of nonwork, we assess its predictions from two perspectives. We …rst confront the model with the most comprehensive measure of joblessness— nonemployment— 2

grouping together nonparticipation and unemployment. This choice is informed by the analysis of Juhn, Murphy and Topel (1991, 2002). While a clear distinction between unemployment and nonparticipation may exist over the business cycle, they argue that the boundary between these two states is blurred at low frequencies. In their words, “[t]he composition of unemployment has shifted toward less skilled workers, who su¤er comparatively long spells of joblessness and whose rewards from work have fallen sharply. In both these respects, they resemble the growing class of men who have simply withdrawn from the labor market” (1991, p. 125). Viewed from this perspective, the model suggests that the combined e¤ects of changes in aggregate wage growth and returns to experience can account for all of the increase from 1968 to 2006 in nonemployment among low-skilled men, and around half of the increase in nonemployment among all men. This view is not the only interpretation of the model, however. The second perspective we consider is to align the labor supply margin that we model with the participation decision, rather than with nonemployment, implicitly grouping together employment and unemployment. Thus, we also examine the extent to which our explanation can account for secular trends in nonparticipation. Rates of nonparticipation among prime-age men in the United States rose profoundly from 4 percent in the late 1960s to 9 percent in the early 2000s (Figure 1C). Mirroring the skill pro…le of nonemployment shown in Figure 1B, the process of detachment from the labor market was concentrated among the low skilled, with high school dropouts facing rises in nonparticipation rates from 5 percent to 20 percent over the same period (Figure 1D). Reassuringly, the model also provides a good account of these trends in male labor force participation, over predicting slightly the rise in trend nonparticipation among low-skilled workers, and accounting for the majority of the secular rise in aggregate male nonparticipation since the 1960s. Hence, our novel channel for relating productivity growth to the employment rate …nds empirical support whether viewed through the nonparticipation or nonemployment data. The plan of the remainder of the paper is as follows. In Section II, we present a very simple model of labor supply in the presence of a return to experience and aggregate wage growth in order to provide the basic qualitative intuition for the e¤ects we emphasize. This theory demonstrates transparently and intuitively how the returns to experience and the aggregate rate of wage growth interact to explain the correlation of the level of the employment rate and the rate of growth of productivity and wages. We also extend the model in Section II to examine whether the presence of labor market frictions may interact with the wage growth channel we emphasize in determining incentives to supply labor. Qualitatively, we show that frictions shade down the e¤ect of wage 3

growth on labor supply, and that reductions in job-…nding prospects discourage labor supply. Quantitively, however, we …nd that the magnitude of these e¤ects is likely to be modest. In Section III, we then present empirical results that con…rm the substantial changes in aggregate wage growth and the return to experience among low-skilled, marginal workers. This section uses Decennial Census and Current Population Survey (CPS) data to study wage growth and the returns to experience for male workers by level of educational attainment. We …nd signi…cant changes in aggregate wage growth and the return to experience that, when combined with our theoretical analysis, help explain the productivity/employment puzzle. A novel empirical …nding is that the lowest skilled workers have experienced declines in the return to experience. Previous work …nds that the return to experience has generally increased. Our empirical work supports this …nding, but shows how these increases in the return to experience are not shared by the least-skilled workers. This …nding is pivotal for our analysis since these low-skilled workers are precisely the population on the margin for the work/not-work decision. In Section IV, we extend the simple model of Section II to account for …nite worker lifetimes, as well as nonlinear experience-earnings pro…les. Using this generalized model, we then draw out the quantitative implications of the observed changes in wage growth documented in Section III for trends in male nonemployment and nonparticipation. In Section V we discuss how this paper relates to the literature. In Section VI, we o¤er conclusions and discuss directions for future work.

II

The Productivity Growth/Employment Interaction: Basic Model

We …rst present a simple model that delivers our basic insights on the interaction of aggregate wage growth and the return to labor market experience, and its role in the determination of incentives for lifetime employment. Consider a simple environment in which there are two employment states, employment and nonemployment, and workers choose whether they want to supply their labor or not. Note that the phenomenon we are aiming to model is the life-long choice that a worker makes to be committed to the labor market and therefore accrue the returns to experience. Consequently, we initially abstract from frictional episodes of unemployment between jobs. The critical addition that we explore relative to previous literature is to allow for two forms of wage growth— aggregate productivity growth and an individual worker’s return to labor market experience— as well as growth in the ‡ow payo¤ from nonemployment. Consider

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an in…nitely lived worker i who must make a once-and-for-all decision at the start of his (non) working life between working forever and not working forever. If he works, he accumulates a year of labor market experience x for every year he works, and faces a wage pro…le wi (x; t). Assume that there is a return to experience gx , and aggregate wage growth gw , such that (1)

ln wi (x; t) = ln wi (0; 0) + gx x + gw t:

It is straightforward to derive equation (1) as the labor demand equation implied by a constant returns to scale production technology with fully ‡exible inputs, in which a worker with experience x accounts for egx x e¢ ciency units of labor, and labor augmenting technical progress occurs at rate gw over time (see Appendix A for a derivation). If the individual decides not to work, he does not accumulate experience, and he receives a payo¤ from nonemployment equal to bi (t). Assume that the latter grows over time at rate gb .2 In this simple environment, all the worker need do is choose the option that delivers the highest present value of lifetime earnings. In particular, if the discount rate is equal to r, it is straightforward to show that a newborn potential worker at time t will decide to work if his o¤ered wage, wi (0; t) exceeds a reservation wage equal to wi (0; t)

wRi (t) = bi (t) , where

r

gw r

gx gb

:

(2)

This simple formulation for the reservation wage relies on an in…nite horizon speci…cation and an assumption of geometric growth in this simple model. In Section IV below, we present a more general model that preserves the intuition of this formulation for the reservation wage while taking into account a more realistic speci…cation of the trajectory of wages.

A

Wage Growth and Steady-State Employment

A number of insights follow from the simple observation in equation (2). First note that, while the reservation wage grows over time at the same rate as the payo¤ from nonemployment, gb , the wage of a newborn worker, w (0; t), grows at the rate of aggregate wage growth, gw . To see the signi…cance of this, imagine an economy populated by workers facing di¤erent wage pro…les, wi (x; t) = ! i w (x; t), and di¤erent payo¤s from nonemployment, bi (t) = i b (t), but 2

In this context, the ‡ow payo¤ from nonemployment b must include much more that unemployment compensation, which has short duration in the U.S. except during deep recessions. Empirically, much of the secular rise in nonemployment in the U.S. is accounted for by increases in very persistent (full-year) nonemployment spells (Juhn, Murphy and Topel, 1991, 2002). In addition, the model we present is one of the life-long decision to work. Possible interpretations of b include the income of other household members, income from employment in turbulent jobs with limited human capital accumulation, the value of home production and leisure, as well as public health insurance, disability insurance and social security.

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who otherwise face the same labor supply problem. The variables ! i and i thus represent heterogeneity in skill and the payo¤ from nonemployment respectively. It follows that the steady-state employment rate in this economy will be given by L = Pr [wi (0; t)

bi (t)] = 1

(

);

(3)

where ( ) is the c.d.f. of the ratio ! i = i , and b (t) =w (0; t) is the replacement rate for newborn workers. For employment to be in steady state, the replacement rate must be stationary. The replacement rate will be stationary only if the growth rate of the payo¤ from nonemployment is equal to the rate of aggregate wage growth, gb = gw in steady state. To see why, imagine for example that gb > gw . In this case, the employment rate will converge to zero over time as the payo¤ from nonemployment increasingly dominates the payo¤ from work. A symmetric logic holds for the case where gb < gw . Imposing the restriction required for a steady state to exist, gb = gw , implies that the reservation wage may be rewritten as wRi (t) = bi (t) , where

1

gx : r gw

(4)

Note that the constraint gw = gb is not special to our formulation. Any model with a steady state will have to impose it. Together, equations (3) and (4) characterize the determinants of incentives to work in this simple environment. We observe that changes in employment are driven by changes in either or . The e¤ects of changes in the replacement rate are simple and well-understood: A higher replacement rate renders nonemployment more attractive and reduces steady state labor supply. This e¤ect is a very conventional long run property of models of equilibrium employment (see Blanchard, 2000; Layard, Nickell and Jackman, 1991, among others). The determinants of the variable are less common in the literature— the return to labor market experience, gx , the rate of aggregate wage growth, gw , and their interaction. We now explore these e¤ects in more detail. Consider …rst the e¤ects of the return to experience. Note from equation (4) that a positive return to experience, gx > 0, drives a worker’s reservation wage below his ‡ow payo¤ from nonemployment. The reason is simple. If workers anticipate positive returns to experience, they will forgo earnings in the short run in order to reap the returns to experience in the long run. This point has long been noted since Weiss (1972), and more recently by Imai and Keane (2004), but has been largely neglected in macroeconomic models where wage growth is linked only to the level of productivity and not to labor market experience.3 3

An adundant literature on post-schooling investment in human capital, based on the seminal work of

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A corollary of this observation is that increases in the return to experience will reduce reservation wages even further below the ‡ow payo¤ from nonemployment, and therefore will lead to increased employment rates. The reason is that increases in the return to experience raise the present discounted value of earnings from working relative to not working. The key implication of (4) that underlies our account for the comovement between productivity growth and employment are the e¤ects of a change in the rate of aggregate wage growth, gw . Equation (4) reveals that there is an interaction between gx and gw : When the return to experience is positive, increases in the rate of aggregate wage growth lead to reductions in reservation wages, thereby raising aggregate employment. The simple reason is that greater aggregate wage growth interacts with the return to experience by compounding the rate of wage growth relative to the growth of the payo¤ from nonemployment. Aggregate wage growth acts like compound interest on the return to experience.4 It is important to note that the latter e¤ect of aggregate wage growth on incentives to supply labor is absent in traditional models of aggregate employment determination which abstract from returns to experience and implicitly set gx = 0. Highighting how a positive return to experience creates an e¤ect of the trend rate of growth on employment is a central contribution of this paper. The perceptive reader will observe that the e¤ect of aggregate wage growth in our model is driven by the speci…cation that experience is multiplicative, not additive, in determining wages, i.e. that the Mincerian wage equation be speci…ed in logarithms rather than in levels. The speci…cation that experience and productivity are multiplicative is, however, much deeper than a functional form restriction. If the returns to experience were additive in wages, i.e., a …xed amount rather than …xed percentage, then the returns to experience would become vanishingly small over time if there is a positive trend to productivity. So a linearly additive speci…cation for experience is equivalent to assuming no steady-state return to experience whatsoever. Ben-Porath (1967) has highlighted the implications of the joint determination of human capital accumulation and labor supply for the life cycle pro…les of earnings and hours worked (Blinder and Weiss, 1976; Heckman, 1976; Ryder, Sta¤ord and Stephan, 1976), education choice (Willis and Rosen, 1979) and the estimation of preference and technology parameters (Shaw, 1989; Lee, 2008). See Weiss and Rubinstein (2006) for a survey. Perhaps most related to the present paper is the analysis of Olivetti (2006), who emphasizes the role of changes in returns to experience among women since the 1970s. In contrast to our analysis of low-skilled males, she …nds evidence of steepening experience-earnings pro…les among women, and identi…es it as a key driving force for increased female labor force participation since the 1970s. 4 The mechanism for the e¤ect of gw on employment incentives, though simple, can appear subtle. A natural question is whether this mechanism requires any more than the usual ingenuity that we ask of individuals when we apply our economic models to the real world. Our sense is that it does not. Individuals in the model do not care about the composition of wage growth between aggregate wage growth, and returns to experience; they only have to keep track of overall growth in wages. The mechanism can appear subtle to economists because we care about delineating the separate e¤ects of gw and gx .

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B

Where Shocks Hit Hardest: The Importance of Marginal Workers

The simple model of this section adds two novel determinants of variation in the aggregate employment rate: the return to experience and the rate of aggregate wage growth. A more precise expression for the e¤ects of changes in gw and gx on steady state employment can be obtained from logarithmic di¤erentiation of (3) to obtain, ln L =

"

ln ;

(5)

where " is the steady state elasticity of labor supply with respect to the wage, "=

0

1

(

) (

)

:

(6)

Note that " is the elasticity of labor supply on the extensive margin, i.e. the employment vs. nonemployment margin. Consequently, it measures the elasticity of the inverse c.d.f. of reservation wages in the economy.5 Thus, we see that the employment e¤ects of changes in the rates of aggregate wage growth and the return to experience are increasing in the size of the wage-elasticity of aggregate labor supply, ". The intuition for this result is simple. A small value of " implies that there are little incentive e¤ects of wages on workers’ choice to supply labor. This in turn extinguishes the labor supply e¤ects of wage growth which rely on the notion that wages incentivize labor supply. The employment elasticity " will be particularly large for workers who are low-skilled. To see this, note that we can write the steady-state employment rate among workers of a given skill ! as L (!) = 1 ( =!) ; (7) where ( ) is the c.d.f. of the inverse of workers’ idiosyncratic payo¤s from not working, 1= i . It follows that the wage elasticity of the employment rate for workers of skill ! is equal to 0 ( =!) : (8) " (!) = ! 1 ( =!) A su¢ cient condition for this elasticity to decline with skill, !, is that the modal worker 5

Focusing on the extensive margin of labor supply abstracts from the possibilities that, facing lower returns to lifetime work, (a) individuals who work may choose to work more hours per week via the income e¤ect and (b) individuals who do not work may have chosen to work if they had the option of working more hours per week.

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of that skill is employed.6 Thus, the model predicts that low-skilled workers respond to changes in the rate of aggregate productivity growth and the return to experience to a greater extent. The simple reason is that low-skilled workers are more likely to be on the margin of the employment decision than high-skilled workers, and therefore are more responsive to changes in the incentives to work. This prediction of the model formalizes the intuition underlying the empirical analysis of Juhn, Murphy, and Topel (1991, 2002). They show that much of the increase in joblessness in the United States from the 1970s onward is concentrated among low-skilled workers, an observation that is replicated in Figure 1B. In addition, they provide estimates of the elasticity of labor supply by skill group (see Table 9 of their 1991 article and Table 10 of their 2002 article) that con…rm that low-skilled labor supply is much more elastic than for higher skilled workers. Both of these results are consistent with the formal implications of our model. We will see later in Section IV that the tight correspondence between our theoretical model and the empirical results of Juhn, Murphy, and Topel will enable to us to interpret and quantify the implications of our model for observed trends in joblessness in the United States over time.

C

Interactions with Labor Market Frictions

Thus far, our analysis has demonstrated the important role of wage growth in shaping reservation wages in a model in which individuals face no frictions to obtaining work. A natural question is whether the existence of labor market frictions may interact with wage growth in determining incentives to supply labor. One of the determinants of the decision to seek work might be the di¢ culty of obtaining work itself. To explore this possibility, in this subsection we extend our basic model to incorporate such frictions. Speci…cally, if employed workers lose their job at rate s, and new job o¤ers arrive at rate f , we show in the Appendix that the reservation wage mirrors equation (4), except that the coe¢ cient is modi…ed slightly: wRi (t) = ~ bi (t) , where ~

1

r + f gw gx : r gw r + s + f gw

(9)

This result motivates a number of observations. First, the addition of frictions shades r+f gw down the e¤ects of wage growth by a factor r+s+f < 1. Intuitively, episodes of frictional gw unemployment impede the accumulation of labor market experience for an individual who 6

To see this, note that since =! is declining in !, the elasticity of aggregate labor supply for workers with skill ! will decline with skill if 00 ( =!) > 0. If ( ) is unimodal, a su¢ cient condition for the latter is that the modal worker with skill ! chooses to work.

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supplies his labor. Second, consistent with the intuition that motivated this extension, r+f gw , raising reservation wages, and reductions in the job-…nding rate lower the factor r+s+f gw disincentivising labor supply. In addition to these qualitative e¤ects, however, equation (9) also provides guidance on the likely quantitative magnitude of these e¤ects. Speci…cally, for empirically-plausible values of the ‡ow transition rates s and f , an excellent approximation to the additional term r+f gw f 7 is simply s+f . A useful interpretation of the latter is that it is equal to one minus r+s+f gw the steady-state rate of frictional unemployment. Thus, a very good intuitive rule of thumb f of his is to imagine that an individual who supplies his labor will be employed a fraction s+f working life, and so will accrue the same fraction of the total possible returns to experience. By the same token, this interpretation clari…es that any interactions between the e¤ects we emphasize and labor market frictions are likely to be modest in magnitude. The reason is f that empirically-plausible values for the rate of unemployment imply values of s+f that are very close to one. This suggests that the e¤ects of wage growth on reservation wages implied by the frictionless model underlying equation (4) are a very good guide to the same e¤ects in the presence of frictions in equation (9). This point does not preclude that changes in wage growth may a¤ect rates of job-…nding, and thereby rates of unemployment, for example via the capitalization e¤ects emphasized by Mortensen and Pissarides (1998) and Pissarides and Vallanti (2007). We return to this point in Section V.8

D

Summary of Qualitative Predictions

This section has used a very simple model to elucidate the e¤ects of wage growth on aggregate employment in an environment that incorporates a return to labor market experience. It has established the following qualitative predictions: First, increases in the rate of return to experience reduce reservation wages and stimulate aggregate employment by increasing the present discounted value of working over not working. Second, if there is a positive return to experience, increases in the rate of aggregate wage growth will also reduce reservation wages and raise aggregate employment. And …nally, the employment e¤ects of wage growth, of the return to experience, and of the interaction of wage growth and the return to experience will be greatest among low-skilled workers who are the most marginal to the employment 7

For example, estimates for prime-age males reported by Fujita and Ramey (2006) suggest job-…nding rates of approximately 0.33 and job-loss rates of approximately 0.015 on a monthly basis. These imply annual job-…nding and job-loss hazards of approximately 4 and 0.18 respectively, dwar…ng analogous values for r and gw . 8 Our approach in this subsection mirrors a recent literature that has sought to incorporate both unemployment frictions as well as a labor supply margin. See, for example, Garibaldi and Wasmer (2005), Krusell, Mukoyama, Rogerson and S ¸ahin (forthcoming), and the references therein.

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decision. The evidence discussed in the next section bears directly on these e¤ects and how they might inform the growth rate/employment puzzle.

III

Evidence

In this section we take on the task of documenting evidence on changes in aggregate wage growth and in the returns to experience by skill for workers in the United States over time. In Section IV, we use this evidence, together with a generalization of the model of Section II, to simulate the e¤ects on employment rates of changes in the return to experience and its interaction with real wage growth.

A

Changes in Aggregate Wage Growth by Skill

To measure changes in the rate of aggregate wage growth we use March CPS microdata for the period 1967 to 2006. We restrict our samples along several dimensions. First, we concentrate on outcomes for white men since labor force participation issues for non-whites and women are signi…cantly more complicated (Smith and Welch, 1989; Welch, 1990; Blau, 1998). In particular, we restrict the samples to non-immigrant white males aged 16 to 64. Mirroring Juhn, Murphy and Topel’s (1991, 2002) in‡uential analyses of wages and employment by skill in the United States, we additionally focus on respondents with fewer than 30 years of potential experience who report that they were out of school for the entire year and are not self-employed. Wages are measured by dividing annual wages and salary by annual hours worked. As our theory makes clear, we are especially interested in changes in wage growth for marginal workers who are relatively low in the skill distribution. We use educational attainment as a proxy measure of skill. We distinguish among high school dropouts (9 to 11 years of education), high school graduates (12 years), those with some college education (13 to 15 years) and those with a college or higher degree (16+ years).9 Finally, to ensure that measured changes in aggregate wage growth are not driven by changes in the experience composition of our samples over time, we compute average wage growth from the distribution of wages reweighted to hold constant the distribution of experience using the method of DiNardo, Fortin and Lemieux (1996). Figure 2 plots trend hourly wage growth by education from 1968 through to 2006 based on these CPS samples. Speci…cally, this takes estimates of real hourly wages by education, computes implied annual wage growth by education, and reports the HP …ltered series. 9

Juhn, Murphy and Topel (1991, 2002) measure skill by percentiles of the wage distribution, rather than by educational groups. Reassuringly, they obtain similar results.

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This exercise reveals a clear picture of aggregate wage growth in recent decades. For all educational groups, aggregate wage growth fell in 1970s, rebounded in the 1980s and 1990s, and has fallen o¤ again in recent years. In addition, we observe that trend wage growth declined more acutely among low-skilled workers in the 1970s. Among high school dropouts, wage growth declined secularly in the 1970s from around 3 percent per year to trend real wage declines of approximately 3 percent in late 1970s and early 1980s. In contrast, real wage growth among college educated workers declined more slowly in the 1970s, and rebounded more robustly in the 1990s.10 These observations echo well-documented facts on aggregate growth, as well as wages by skill. The secular decline and subsequent rebound in aggregate wage growth over time mirrors the productivity slowdown of the 1970s as well as the so-called “productivity miracle” of the 1990s in the United States. Figure 2 overlays the trend productivity growth rate over the same period to emphasize these trends. Likewise, the observation that wage growth declined more sharply among the low-skilled in the late 1970s and 1980s is consistent with the widely documented increase in wage inequality that emerged over that period.

B

Changes in the Experience-Earnings Pro…le by Skill

To measure changes in the experience-earnings pro…le over time, we employ data taken from the decennial Censuses from 1960 to 2000, and the American Community Surveys from 2001 to 2007 for the United States.11 Earnings are measured by the annual wage and salary income of respondents. Mirroring our analysis of aggregate wage growth, we again proxy skill using discrete education categories: high school dropouts (9 to 11 years), high school graduates (12 years), some college (13 to 15 years), and college degree or higher (16+ years). Experience is measured by potential experience, i.e. age minus years of education minus six. We focus on the return to experience among full-time, full-year workers, de…ned as those who work 35 hours or more per week, and who are employed for 50 or more weeks per year. We do this for a number of reasons. By focusing on such workers, we can be more con…dent that respondents have left full-time education when we observe their earnings. 10

A potentially important confound to the trends in Figure 2 is the growth of non–wage compensation (such as health insurance, pensions and paid leave) that emerged over the period. It is di¢ cult to get an accurate sense of this from the data sources we use. However, using the microdata underlying the Employment Cost Index, Pierce (2001) shows that wage growth understated compensation growth among high–skilled workers in the 1980s, but that it overstated compensation growth among the low–skilled in the 1990s. Hence, for total compensation the relative growth rate in wages for low-skilled workers is likely to be even less favorable than shown in Figure 2. 11 Our Census samples are taken from the public use 1% sample for 1960, 2% sample for 1970, and 5% samples for 1980 to 2000 available from IPUMS. They parallel those used by Heckman, Lochner, and Todd (2007) in their important study of the returns to schooling. We are grateful to those authors for providing us with detailed tabulations from their work that we used in the preliminary version of this paper.

12

Moreover, the observed pro…les are more likely to re‡ect variation in wages rather than hours or weeks worked. Finally, the fact that we are able to measure only potential experience raises a concern that a changing relationship between potential and actual experience could confound observed changes in experience-earnings pro…les. By concentrating on full-time, full-year workers, such a confound is minimized. Figure 3 plots average log earnings as a function of potential experience by education group, normalized to the mean log earnings of workers entering the labor market. Log earnings are normalized to equal zero at zero experience to abstract from the signi…cant di¤erences in levels of earnings across education groups and of aggregate wages across time. These levels shifts in wages do not a¤ect equilibrium employment in our model. Within each panel, the lines correspond to the experience-earnings pro…les for di¤erent Census years for a given education group.12 Figure 3A displays the experience-earnings pro…le for high school dropouts (9-11 years of education) over time. Note that outcomes for these lowerskilled workers are of particular interest for our purposes because they are more likely to be marginal to the employment decision. Figure 3A tells a striking story. The experienceearnings pro…le among high school dropouts ‡attened dramatically after 1970. At …ve to ten years of potential experience, earnings are around 50 log points lower in the later period compared to the earlier period. In addition, the gap in the experience-earnings pro…le persists at higher levels of experience. Figure 3B plots the experience pro…le for high school graduates. This reveals a mild drop in mid-career earnings between 1970 and 1990, with a more substantial drop in the experience-earnings pro…le between 1990 and 2000. In comparison to the outcomes for high school dropouts, the changes are relatively modest.13 As emphasized above, workers with schooling beyond high school are unlikely to be at the point in the skill distribution where employment is a marginal decision, so that patterns in experience-pro…les among these groups are less relevant to employment rates. By way of comparison, however, we include results in Figures 3C and 3D for workers with some college 12

Prior to 1980, Census data record only hours last week, and after 1990 only usual hours of work. Reacting to this, we impose the full-time restriction for the 1960 to 1990 pro…les based on hours last week. After 2000, we compute the di¤erence in the experience–earnings pro…le generated by implementing the full-time restriction using these alternative hours measures in 1990, when both measures are available. We then apply that di¤erence to impute the experience–earnings pro…les from 2000 on. 13 For high school graduates and college educated workers, a number of studies in the empirical literature on changes in wage inequality has estimated the “experience premium,” measured as the log wage gap between experienced workers (typically with 25 years of experience) and less experienced workers (5 years of experience) using CPS data (see, for example, Katz and Autor, 1999; Weinberg, 2005; Autor, Katz and Kearney, 2008). These studies all have documented evidence for a rise in the experience premium among high school graduates and college graduates over time. The evidence presented in Section III and Appendix B shows the new …nding that the returns to experience among high school dropouts have declined since 1970 and also con…rms the …ndings of this earlier literature for higher-educated workers.

13

education and a college degree or higher respectively. For these higher skilled workers, an opposite trend can be discerned, especially for college educated workers, with experienceearnings pro…les steepening over time. A number of questions arise in the light of the substantial decline in the experienceearnings pro…le for high school dropouts in Figure 3A. First, in Appendix B, we consider the robustness of the result to a range of possibilities, including: a widening gap between potential and actual experience driven by the increases in joblessness documented in Figure 1; selection associated with the possibility of high school dropouts becoming less-skilled over time; and consistency with alternative measures of the experience premium. On all these dimensions, we …nd that the central message that the experience-earnings pro…le for high school dropouts has ‡attened substantially remains robust. Second, given the robustness of this result, one might ask how big a reduction this is. A natural way to quantify the decline is to compute the capitalized value of the experienceearnings pro…les illustrated in Figure 3A. Figure 4 performs this exercise. It plots the capitalized value of the experience-earnings pro…les in Figure 3A, normalized to equal 100 in 1970, for a range of values for the discount rate. A clear picture emerges: Regardless of the discount rate, the value of the experience-earnings pro…le for high school dropouts declined by almost 50 percent between 1970 and 2007, a substantial reduction.

C

Synthetic vs. Actual Cohorts

The preceding results report cross-sectional experience-earnings pro…les at given points in time. For the purposes of our analysis of the likely employment e¤ects of any changes in these pro…les, we would like to obtain information on workers’ expectations of their likely experience pro…le at the time that they are making their labor supply decisions. It is likely that these cross-sectional pro…les are informative to some degree on these expectations— for instance, if workers have static expectations or changes are permanent, so that static expectations are rational. An alternative way of slicing the data, however, would be to plot the realized experienceearnings pro…les of individual cohorts. This alternative approach would be consistent with workers’expectations if they were endowed with perfect foresight. The truth, of course, is likely to lie somewhere between these two extremes, so it is natural to check whether the basic message of the data changes by shifting perspective in this way. Figure 5 presents the realized experience-earnings pro…les for the cohorts entering the labor market in 1960, 1970, 1980, 1990, and 2000. Since the Census data we use is available

14

only at a decadal frequency, we plot earnings for members of these cohorts every 10 years.14 For high school dropouts, while the cohort pro…les in Figure 5A are noticeably ‡atter after ten years of experience, the trends across cohorts tell exactly the same story as the crosssectional picture in Figure 3A. Wage growth declines for each consecutive cohort entering the labor market after 1960, and the declines are of similar magnitude as those indicated by the cross-sectional pro…les in Figure 3A. These cohort-based pro…les mirror the …ndings of Kambourov and Manovskii (2009) using CPS and PSID data. The pro…les for high school graduates, and those with college education in Figures 5B, 5C and 5D also echo the patterns observed in their cross-sectional counterparts in Figure 3. Most noticeably, it is again possible to discern a steepening of experience-earnings pro…le among younger cohorts of college graduates. It is reassuring that these two di¤erent slices of the data have similar implications with respect to the changes in returns to experience over time.

IV

Quantitative Implications

To what the extent do the changes in aggregate wage growth and experience-earnings pro…les documented in Section III account for changes in the rate of nonemployment documented in Figure 1? In this section, we extend the simple model of Section II. The extended model retains the transparent qualitative predictions of the simple model while adding enough generality to allow for analysis based on the earnings pro…les quanti…ed in Section III.

A

A More General Model

The model of the Section II is simpli…ed in a number of respects. In this section we relax some of these simplifying assumptions. First, we allow for …nite worker lifetimes. This enables discussion of the di¤erential e¤ects of changes in wage growth across di¤erent cohorts of workers in a natural way. Second, we allow the return to experience to be nonlinear to allow for the concavity of the experience-log earnings pro…le observed in Figures 3 and 5. This allows us to match the experience-earnings pro…le in the model with that observed in the data. Third, we allow workers to choose whether to work or not at each point in their lives, thereby relaxing the once-and-for-all labor supply decision of Section II. Extending the model in this manner allows us to draw out the dynamic e¤ects of changes in rates of wage growth on employment in and out of steady state. Though more realistic, we will see that these changes do not change the basic qualitative message of the simple model of Section II. 14

Additionally, we impute data points for 2010 under the assumption that the experience–earnings pro…le in 2010 will be the same as that in the pooled 2001 to 2007 ACS samples.

15

Consider a worker entering the labor market at time s with a working life of length T . At each point in time the individual chooses whether he wants to work (h = 1) or not work (h = 0). As in the model of Section II, for every year he works, he accumulates a year of labor market experience, x; he does not accumulate experience while not working. A worker of experience x at time t receives a ‡ow wage equal to w (x; t).15 An individual who does not work at time t receives a ‡ow payo¤ b (t). The worker makes his labor supply decision in order to maximize the present discounted value of his lifetime income. Thus, we can state the optimization problem of an individual entering the labor market at time s as follows: max h(t)

Z

s

s+T

e

r(t s)

y (x; t; h) dt s.t. x_ = h, h 2 f0; 1g , x (s) = 0;

(10)

where r is the real interest rate. The individual’s income at time t is given by y (x; t; h) = hw (x; t) + (1 h) b (t). If the individual works (h = 1) he receives the wage; otherwise, he receives the payo¤ from not working. The …rst constraint in (10) regulates the accumulation of experience over the worker’s lifetime such that experience is accumulated only when the individual works. The second emphasizes our focus on the extensive margin of the labor supply decision. And the third constraint states the initial condition that new entrants into the labor market enter with no accumulated experience. The maximization problem in equation (10) can be restated more simply as an optimal control problem with associated Hamiltonian H (x; t; h; ) = hw (x; t) + (1

h) b (t) + h:

(11)

Note that the Hamiltonian is linear in the labor supply variable, h. It follows that an individual with experience x at time t will work if the wage o¤er w (x; t) exceeds a reservation wage given by wR (t) = b (t) (t) ; (12) where we will see that (t) 0. Thus, just as in the simple model of Section II, we observe that the reservation wage lies below the ‡ow payo¤ from nonemployment. As before, individuals are willing to forgo payo¤s in the short run in order to reap the returns to experience in the long run. To characterize the reservation wage more precisely, however, we must describe the variable in more detail. Using the principles of optimal control, it is simple to show that 15

In this more elaborate model, we suppress the i subscript that indexes individuals for purposes of clarity.

16

can be expressed as16 (t) =

Z

s+T

e

r(

t)

h (x ( ) ; ) wx (x ( ) ; ) d :

(13)

t

Thus, has a very intuitive interpretation. It is the cumulative discounted sum of future returns to experience, wx (x ( ) ; ), taking into account that these future returns accrue only in the event that the individual works in the future (h (x ( ) ; ) = 1). In short, is the marginal value of experience to a worker. This simple interpretation in turn delivers a simple interpretation of the reservation wage. In particular, we can rewrite the reservation wage as wR (t) = b (t)

Z

s+T

e

r(

t)

h (x ( ) ; ) wx (x ( ) ; ) d :

(14)

t

Thus, the reservation wage is equal to the ‡ow bene…t from not working, b (t), less the opportunity cost of not working, which equals the foregone returns to experience. As stated, the reservation wage is a very forward looking object— it depends on the entire sequence of future labor supply decisions from time t until the end of the individual’s life, s + T . To obtain a more concrete sense of the form of the reservation wage, we need to partition the individual’s remaining lifetime into episodes allocated respectively to employment and nonemployment. This is aided by the following result: Proposition 1 If (i) r gw > 0, so that workers discount the future; (ii) the experienceearnings pro…le is monotonically increasing;17 and (iii) there are no shocks, then a worker who decides to work at time t subsequently will work for the remainder of his working life. Intuitively, consider an individual who is just about to start working. By de…nition, such an individual only just prefers working over not working. As the individual works, however, he accumulates human capital which in turn serves only to make employment increasingly preferable relative to not working. As a result, the individual continues to work until he retires. From the principles of optimal control, we can write _ = r (t) @[email protected] = r (t) h (x; t) wx (x; t). The solution to this di¤erential equation is given in equation (13). The constant of integration is equal to zero because of the transversality condition that (s + T ) = 0. 17 Assuming that wx (x; t) > 0 for all x and t is not entirely innocuous. Evidence suggests that average real wages can decline with experience at the end of a worker’s career. However, it is not clear whether this is driven by (partial) retirement. For the horizons we focus on in what follows (the …rst forty years of working life) nondeclining wages is not a bad assumption. An extension of the model to account for optimal retirement would be an interesting topic for future research. 16

17

In the light of this, we adopt the convention that, whenever the individual is o¤ered his reservation wage, he works thereafter. It follows that, for an individual with experience x at time t, we can substitute h (x ( ) ; ) = 1 and x ( ) = x + t for all > t into the reservation wage equation above to derive wR (x; s; t) = b (t)

Z

s+T r(

e

t)

wx (x +

(15)

t; ) d :

t

To complete our characterization of the reservation wage, we must be more explicit about the form of the wage equation. Denoting aggregate wage growth by gw , and the return to experience at x years of experience as gx (x) @ ln w (x; ) [email protected] allows one to write wR (x; s; t) = where

(x; s; t) b (t) , (x; s; t) = 1 +

Z

s+T

e

t

R

t

1 [r gw gx (x+z t)]dz

gx (x +

t) d

:(16)

Although the form of the reservation wage in this more general model is not as transparent as equation (4), a number of observations can be made in the light of it. First, note that the reservation wage takes a form that is reminiscent of equation (4) from the simple model of Section II. The reservation wage is equal to the ‡ow payo¤ from not working b (t), scaled down by a factor (x; s; t) 1. As emphasized before, workers are willing to forgo current earnings to reap the returns to experience in the future. The return to experience drives a wedge (x; s; t) between the payo¤ from nonemployment and the reservation wage. Second, note that in the case where individuals are in…nitely lived, T ! 1, and the return to experience is constant for all levels of x, gx (x) gx , then (x; s; t) ! 1 [gx = (r gw )] = from equation (4). Thus, the general model nests the simple model of Section II as a special case.18 Third, we again observe that changes in the experience-earnings pro…le, summarized by gx ( ), and aggregate wage growth, gw , a¤ect the reservation wage. As before, increases in the experience-earnings pro…le and aggregate wage growth reduce (x; s; t), thereby lowering the reservation wage and stimulating work incentives. Equation (16) is di¤erent from equation (4) because it takes into account …nite lifetimes and concave experience-earnings pro…les, leading to more sensible magnitudes of these e¤ects. Fourth, a key message of equation (16) is the implied life-cycle e¤ects of changes in gx ( ) and gw . Speci…cally, the marginal e¤ects of these changes on the reservation wage are stronger for younger cohorts at a given point in time t and weaker for older cohorts. To see 18

Note also that the once-and-for-all labor supply assumption in the simple model of Section II is therefore not a binding one. This, of course, follows from Proposition 1.

18

this, consider equation (16) and recall that s denotes time of entry into the labor market, so that higher values of s refer to younger cohorts. Mechanically, this result arises because older workers have a shorter remaining working life over which changes in wage growth of any variety can a¤ect the present value of their remaining earnings stream. More intuitively, as workers age, they become increasingly less marginal to the employment decision, and consequently respond less to changes in wage growth.19 We will see in what follows that these life-cycle e¤ects have distinctive implications for the dynamics of employment generated by the model. Finally, to parallel the analysis of Section II.C., the Appendix presents an analogous solution for the reservation wage that generalizes the more elaborate model of this section to allow for labor market frictions. Mirroring the results of Section II.C., it shows that the existence of frictions has a quantitatively modest e¤ect on the reservation wage in the more general model.

B

Simulations

The results of Section III documented evidence for reductions in the return to labor market experience for low-skilled, marginal workers since 1970, as well as important changes in aggregate wage growth for such workers over the same period. We now seek to provide a quantitative sense of the implications of these trends for work incentives and equilibrium employment. To do this, we feed the observed trends in the experience-earnings pro…le and aggregate wage growth into a simulated version of the general model summarized in equation (16). Since the trends in the aggregate nonemployment rate are driven by the increase in nonemployment among low-skilled workers, we focus …rst on generating the implied outcomes for high school dropouts. We set the length of a working life to 40 years, and initialize the model in steady state in 1968. We set the initial steady-state employment rate to equal 90 percent based on the observed trend nonemployment rate for high school dropouts in 1968 (see Figure 1B). We then compute the implied paths of the employment rate for each experience x, cohort s and time t con…guration by extending the simple insight of equation (5): ln L (x; s; t) =

"

where variation in the reservation wage coe¢ cient 19

ln (x; s; t) ;

(17)

(x; s; t) is induced by variation in aggre-

By the same token, it is also true that the reservation wage coe¢ cient (x; s; t) is larger for older cohorts. One might imagine that this reduces work incentives for older workers. However, we know from Proposition 1 that any individual who starts working will work until retirement. The reason is the wage growth that workers receive as they accumulate experience.

19

gate wage growth gw and the experience-earnings pro…le gx ( ). Finally, we aggregate across (x; s; t) cells to compute the path of aggregate employment, L (t). Our simulation procedure therefore requires …nding a value of ", the elasticity of labor supply. Recall from our earlier discussion that, for our purposes, " is the elasticity of labor supply on the extensive margin— the elasticity of the inverse distribution function of reservation wages (see equations (6) and (8)). Estimates of " for di¤erent skill groups are reported by Juhn, Murphy and Topel (1991, 2002). Speci…cally, they compute estimates of the elasticity of the fraction of a year spent in employment with respect to wages by skill using CPS data. Juhn, Murphy and Topel measure skill by ranges of percentiles of the wage distribution. Since high school dropouts lie in the bottom 20 percent of the education distribution, Juhn, Murphy and Topel’s estimates suggest that a reasonable value of " is approximately 0.33.20 It is worth noting that our simulation strategy has a number of virtues. First, by reducing the procedure down simply to obtaining a value for ", we have avoided having to calibrate explicitly variables such as the replacement rate , or the distribution of worker heterogeneity ( ) in equation (3). Since we might be less con…dent in the correct calibration of these objects, this is a useful simpli…cation. In addition, the simulation strategy is very transparent. If one has di¤erent priors about the appropriate value for the supply elasticity ", all one need do is scale the implied employment e¤ects up or down accordingly. For example, if one believed " were double the value we use, then the implied employment e¤ects will be double what we report. i.

A Simple Example

To get a sense for the dynamic response of aggregate employment implied by the model, we …rst consider the e¤ects of a very simple shock. Figure 6 plots the response of aggregate nonemployment to a one-time, permanent, unanticipated decline in aggregate wage growth gw from 3 percent (as observed in the early 1970s among dropouts) to –3 percent (as observed in the mid 1980s among dropouts). The dashed line plots the steady state nonemployment rate before and after the shock. This rises substantially from 10 percent to approximately 20 percent. 20 To do this, Juhn, Murphy and Topel (1991, 2002) estimate the wage o¤ers of those out of employment. They do this by imputing wages to nonworkers using the distribution of wages among individuals who worked between 1 and 13 weeks in a given year. Table 10 of their 2002 Brookings paper reports partial elasticities (i.e. the change in employment divided by the log change in wage) by skill percentiles for the years 1972 to 2000. For the 1st to 10th percentile, their estimate of the partial elasticity is 0.287; for the 11th to 20th percentile, 0.217. The average employment rates for these groups respectively are 0.73 and 0.80. These imply elasticities of approximately 0:287=0:73 = 0:39 and 0:217=0:80 = 0:27 respectively. Our choice of " = 0:33 is an approximate midpoint of these estimates.

20

The response of the nonemployment rate out of steady state, however, reveals important transitional dynamics in the model. On impact, a discrete fraction of workers immediately leaves employment, deciding that the reduction in lifetime earnings renders working no longer worthwhile. Subsequently, the nonemployment rate exhibits very slow transitional dynamics, eventually reaching the new steady state after 40 years. These transitional dynamics are a direct consequence of the life-cycle response to shocks emphasized in the general model above. As workers age, they become increasingly less marginal to the employment decision, and thereby become less responsive to shocks. What is driving the dynamics in Figure 6 is the turnover of successive cohorts in the labor market as older cohorts retire, and younger, more marginal workers enter. The period of transition is exactly 40 years, the speci…ed length of a working life, since that is the time it takes for all older cohorts at the time of the shock to leave the labor market. ii.

Implications for Low-Skilled Nonemployment

We can now address the question of the e¤ects of observed changes in the experience-earnings pro…le and aggregate wage growth for rates of nonemployment. We begin with results for high school dropouts, who are more likely to be marginal to the work/non-work decision. In this …rst simulation, we match the return to experience in the model, gx ( ), to smoothed versions of the cross-sectional pro…les for high school dropouts in Figure 3A. Aggregate wage growth in the model, gw , is matched to trend wage growth among high school dropouts based on the estimates in Figure 2. We initially feed these trends into the model as a series of unanticipated shocks. Figure 7A displays the results of this simulation based on these unanticipated shocks, together with the trend nonemployment rate among high school dropouts from Figure 1B for comparison. The model predicts a substantial rise in the nonemployment rate for lowskilled workers. Figure 7A reveals that the joint trends in gx ( ) and gw together imply an increase in low-skilled nonemployment from 10 percent to 27 percent between 1968 and 2006. Comparing these outcomes to the observed trend from the data, this suggests that the model can account for all of the secular rise in nonemployment among high school dropouts over this period. Thus, variation in the returns to experience together with changes in the rate of aggregate wage growth have the potential to go a long way toward explaining the long-run variation in nonemployment for low skilled workers in the context of this model. Figure 7A also plots the implied trends in nonemployment from allowing the return to experience and aggregate wage growth to vary separately. This decomposition suggests that, between 1968 and 2006, changes in aggregate wage growth and experience-earnings pro…les accounted for about an equal share of the implied increase in low-skilled nonemployment 21

in the model. However, it also reveals that the e¤ects of gw are relatively more important earlier on, whereas the return to experience plays more of a role later on. This …nding is consistent with the trends depicted in Figures 2 and 3A. Declines in aggregate wage growth occur predominantly in the early part of the sample period, whereas declines in the return to experience among dropouts occur much more uniformly over the period. Another feature of the results in Figure 7A is that the model is less successful in matching the observed timing of the increase in trend nonemployment among high school dropouts. The data reveal a substantial medium run rise in nonemployment in the 1970s and 1980s that the model does not fully predict. We do not necessarily view this as a problem, as it provides room for other explanations to play a role, a point we return to in Section V when we discuss how our explanation dovetails with prior literature. The model’s inability to predict the medium run rise in joblessness also may be related to our choice to feed variation in gx ( ) and gw through the model as unanticipated shocks. It is possible that some of these changes may eventually have been anticipated. For example, workers may have become wise to the downward trend in aggregate wage growth seen in Figure 2. This would speed up the response of nonemployment to these shocks. To highlight this point, we consider an alternative simulation. As before, the labor market is assumed to be in steady state at the beginning of the simulation in 1968. In this case, however, we assume that the time path of aggregate wage growth gw in Figure 2 is subsequently realized by all cohorts. Symmetrically, instead of using the cross sectional experience pro…les from Figure 3, we reveal smoothed versions of the realized experience pro…les to successive cohorts of workers.21 Figure 7B displays the results of this simulation based on these anticipated shocks to wage growth. Consistent with the intuition above, it can be seen that implied nonemployment in the model tracks the medium run rise in nonemployment in the data remarkably well, though implied joblessness in the model overshoots the data in the late 1990s. iii.

Implications for Nonemployment by Skill

Up to now, we have focused on implied trends in joblessness among low-skilled high school dropouts. In this subsection, we compute implied trends in nonemployment rates for the remaining skill groups. Our simulation procedure mirrors exactly the method described above for high school dropouts. For each skill group, we feed the observed changes in the experience-earnings pro…le and aggregate wage growth in Figures 2 and 3 through the model as a series of unanticipated shocks. The only adjustment made is for di¤erences in the extensive elasticity of labor supply " across skill groups. The results of Section II.B. lead 21

Since this simulation uses the realized cohort experience pro…les, it can be peformed up to 2000 only.

22

us to expect that " declines with skill, as more skilled workers are less marginal to the employment decision. The estimates reported in Juhn, Murphy and Topel (1991, 2002) con…rm this intuition. Based on those estimates, we apply values of " equal to 0.2, 0.1, and 0.066 respectively for high school graduates, those with some college education, and those with a college degree or higher. Again, note that the e¤ects of di¤erent assumptions on the magnitude of these elasticities are simply to rescale our reported employment e¤ects up or down respectively. Figure 8 plots trend nonemployment rates implied by our simulations, together with trend nonemployment rates from the data. Figure 8A repeats Figure 7A for ease of comparison. Figure 8 suggests that observed trends in experience-earnings pro…les and aggregate wage growth can account for around 5 of the 10 percentage point increase in nonemployment among high school graduates, and 3 of the 5 percentage point increase for those with some college education. Consistent with the relative stability of the experience-earnings pro…les for these groups in Figure 3, the majority of the implied increase in joblessness among both groups is driven by declines in aggregate wage growth. Figure 8 also reveals that trends in either form of wage growth can explain none of the 2 to 3 percentage point increase in nonemployment among college graduates. The reason, of course, the participation of highskilled workers is not elastic because so few of them are on the work/non-work margin.22 iv.

Implications for Overall Nonemployment

The simulation results allow us to gauge the extent to which variation in wage growth can account for the increase in aggregate nonemployment depicted in Figure 1A. We take a share-weighted average of the simulations in Figure 8. These simulated changes in the nonemployment rates by education group aggregate to 3.4 percentage points— a little more than half of the 6 percentage point rise observed in Figure 1A. Hence, taken together, the mechanisms identi…ed in the paper can account for all of the increase in nonemployment among white male high school dropouts, and for approximately one half of the increase in the aggregate nonemployment rate over between 1968 and 2006. 22 In the working paper version of this paper (Elsby and Shapiro, 2009), we also explore the age structure of the rise in nonemployment. In the model, older workers are less responsive to wage growth shocks, because they have a smaller impact on their remaining lifetime earnings. Consistent with this, rates of nonemployment among men aged 16 to 45 rose earlier and more rapidly among younger workers. For those aged 46 to 55, however, the model undepredicts the rise in nonemployment. This feature of the data is consistent with an abundant literature that has emphasized, to di¤ering degrees, the role of changes in the generosity of disability insurance in declining labor force participation among older prime aged men (Bound, 1989; Bound and Waidmann, 1992; Autor and Duggan, 2003). In the context of our model, this would correspond to a change in b, the payo¤ from not working. Since we abstract from changes in b, we would not expect our simulations to account for all the changes in nonemployment, such as the well-documented decline in employment for older workers resulting from an expansion in disability payments.

23

An important aspect of the simulations is that they take into account the dynamics of the adjustments to changes in growth in wages and the return to experience. As seen in Figure 6, these dynamics can be quite slow. Taking them into account is crucial for understanding the movement in employment rates. In the simulations, the upturn in wage growth has a very delayed e¤ect on aggregate employment rates owing to the decisions of older workers made well before the wage growth increased. Consequently, the upturn in wage growth exhibited in Figure 2 does not lead to a contemporaneous reversal of the decline in employment. v.

Implications for Nonparticipation

Until now, we have interpreted the predictions of the model as being aligned with secular trends in nonemployment— the sum of nonparticipation and unemployment. This is motivated by in‡uential research noting that the distinction between unemployment and nonparticipation has become blurred at low frequencies, as low-skilled unemployed workers increasingly have become detached from the labor market, reporting very long spells of unemployment (Juhn, Murphy and Topel, 1991, 2002). However, as we noted in the introduction, an alternative view would be to interpret the labor supply margin that we model as corresponding to the participation margin. There are institutional, measurement, and theoretical considerations that potentially blur the distinction between nonparticipation and unemployment. While we incline to the the Juhn, Murphy and Topel perspective, the alternative perspective that the labor supply margin addressed by our model bears more directly on nonparticipation has substantial merit. Hence, in this subsection we explore the predictions of our model when viewed through the lens of trends in nonparticipation. Our simulation approach mirrors the preceding analysis of nonemployment; the results are depicted in Figure 9. Nonparticipation among low-skilled high school dropouts is predicted by the model to rise substantially from 5 percent in the late 1960s to 24 percent in the mid 2000s. This tracks the increase seen in the data quite closely, though over predicts slightly the rise in nonparticipation by 2 to 4 percentage points over time. As in the results in Figure 8, declines in returns to experience and aggregate wage growth appear to account for roughly equal parts of the rise in low-skilled nonparticipation, with the productivity slowdown the more dominant earlier in the period. For the remaining skill groups, the model accounts for 4.5 of the 8 percentage point rise in nonparticipation among high school graduates, and for 3 of the 4 percentage point rise among those with some college. As in the results for nonemployment in Figure 8, almost all of the rise in nonparticipation predicted by the model for these workers can be traced to declines in aggregate wage growth that accompanied the productivity slowdown, re‡ecting the more modest changes in the experience earnings pro…le among these skill groups compared to high 24

school dropouts (Figure 3). Taking a share-weighted average of these predicted e¤ects suggests that the model predicts 4 of the 5 percentage point rise in aggregate nonparticipation among prime-age men. Thus, viewed from either the participation margin or the employment margin, the model is able to account for a substantial fraction of the rise in labor force detachment among American men since the late 1960s. The model is able to account for a larger fraction of the secular rise in nonparticipation than in nonemployment, however. The simple reason is that the long-run increase in nonparticipation across skill groups is slightly smaller than that for nonemployment.

V

Related Literature

This paper identi…es a novel explanation for why reductions in trend productivity growth are associated with secular declines in rates of employment. A natural question is how this new explanation contrasts with existing stories for the decline in male employment, and its coincidence with the productivity slowdown.

A

Search, creative destruction and capitalization e¤ects

As noted in the introduction, an important class of models of labor markets with frictions has explored the link between productivity growth and unemployment. As emphasized by Mortensen and Pissarides (1998), the predictions of these models rely crucially on the degree to which new technologies are embodied in newly-created jobs. In models of creative destruction (Aghion and Howitt, 1994), the productivity of a job is …xed according to the state-of-the-art technology available upon creation of the employment relationship. In order to update productivity back to the frontier, older relationships must be severed, hence “creative destruction.” A drawback to models in this vein is that they can have counterfactual predictions with respect to the e¤ects of productivity growth on rates of worker reallocation and the level of unemployment (Blanchard, 1998). Viewed through the lens of these models, declines in productivity growth, such as the slowdown in the 1970s, imply that the rate at which jobs become obsolete slows, reducing job destruction, and thereby unemployment. In contrast to these predictions, the productivity slowdown in the United States was characterized by increased rates of job destruction and increased unemployment.23 23

For example, the data analyzed by Davis (2008) reveal that rates of job loss in the U.S. rose secularly in the 1970s and 1980s when the productivity slowdown occurred, a trend that reversed in the late 1980s and 1990s when productivity growth rebounded.

25

If new technologies may be incorporated into jobs of all vintages, however, a capitalization e¤ect can arise (Mortensen and Pissarides, 1998). The idea is that the creation of new jobs involves the costly process of …lling a vacancy. These costs are borne upfront and are set against the stream of future pro…ts generated by the employment relationship. A slowdown in productivity growth raises the rate at which these future pro…ts are discounted, reducing the returns to job creation, and raising unemployment.24 The mechanism put forward in the present paper complements this capitalization e¤ect in a number of respects. First, the two approaches capture quite di¤erent aspects of the decline in employment that followed the productivity slowdown. The capitalization e¤ect noted by Mortensen and Pissarides (1998) emphasizes the impact of declines in trend growth on the demand for labor over the long run. In doing so, it seeks to provide an account of the rise in episodes of frictional unemployment that accompanied the productivity slowdown. In contrast, the view put forward in this paper provides an account of the decline in labor market attachment, and the concomitant rise in long jobless spells, that were observed in the wake of the slowdown in productivity growth. Accordingly, the emphasis in the present paper is on the e¤ects of aggregate wage growth on incentives to supply labor. Second, the analysis of Section II.C. revealed that the existence of labor market frictions was likely to have only a modest e¤ect on the impact of wage growth on reservation wages that we emphasize. The absence of such interactions suggests that the implications of our theory are approximately additive with the capitalization e¤ects emphasized by Mortensen and Pissarides (1998), which operate through their e¤ects on labor market frictions, in particular the job-…nding rate. Finally, the results of Section IV revealed that the model of this paper could account for the magnitude of the secular rise in nonemployment among the lowest-skilled education group. This is precisely the subgroup of the labor market on the margin of the work/nonwork decision that experienced signi…cant rises in long jobless spells (Juhn, Murphy and Topel, 1991, 2002), which in turn is also the phenomenon our model seeks to encapsulate. In contrast, the model could account for around one half of the increase in aggregate nonemployment. The results of our quantitative analysis therefore leave room for other potential explanations, such as the capitalization e¤ect emphasized by Mortensen and Pissarides. In their quantitative analysis, Pissarides and Vallanti (2007) …nd that plausible calibrations of the capitalization e¤ect can account for part of the empirical relationship between unem24

Manning (1990) identi…es a capitalization e¤ect in a di¤erent context within a dynamic model of union bargaining. In his model, slower productivity growth reduces the future rents from employment available to workers. Consequently, unions capture rents in the present, raising wage pressure, and increasing unemployment.

26

ployment and trend growth, perhaps around one third.25 This, in turn, leaves room for the e¤ects emphasized in the present paper and vice versa. Overall, this suggests that these two explanations are largely complementary, both in terms of being conceptually distinct, and in terms of their quantitative predictions.

B

Does the short run last a long time?

Perhaps because traditional models tend to predict no long run employment e¤ects of changes in productivity growth, a prominent feature of previous literature has been in its emphasis on the potential short run employment e¤ects of variation in productivity growth (see among others Blanchard, 2000; Bruno and Sachs, 1985; Ball and Mo¢ tt, 2001). A popular idea that has been pursued is that the wage demands of workers are somewhat sluggish in their response to changes in productivity growth. Blanchard (2000) has suggested that a “comprehension lag”can arise between the moment of an initial decline in productivity growth and the time that workers become aware of it. Similarly, Ball and Mo¢ tt (2001) have emphasized the possibility of sluggish “wage aspirations” that do not adjust immediately to declines in the sustainable rate of aggregate wage growth. Both of these possibilities will lead to a short run rise in joblessness. Moreover, depending on the sluggishness of reservation wages, the short run can last a long time. A limitation to this approach, emphasized in Blanchard (1998), is that it becomes dif…cult to explain very persistent declines in employment following a productivity slowdown, unless one is willing to impose extreme forms of sluggishness in reservation wages. Such a task becomes especially di¢ cult given the observed rebound in aggregate wage growth that accompanied the productivity “miracle”of the 1990s. Models of sluggish adjustment in reservation wages would predict reductions in joblessness in the 1990s. There was a decline in unemployment across the board in the late 1990s, though not for a long-enough period to change much the picture of trends in nonemployment shown in Figure 1. Interestingly, our model contrasts with these predictions. The results of Section IV imply that the productivity slowdown of the 1970s led to increased joblessness over long (thirty year) horizons, rather than short horizons. Thus, while models of sluggish adjustment in reservation wages may account for the short to medium run rise in joblessness in the 1970s and 1980s, our model can account for the persistent rise in nonemployment into the 1990s. Recall that this is driven by the important employment dynamics that are emphasized when one takes into account the e¤ects of human capital accumulation on work incentives over the lifecycle. 25

Pissarides and Vallanti (2007) …nd that calibrations of the capitalization e¤ect can account fully for the empirical relation between unemployment and productivity growth only if jobs last almost inde…nitely, and wages are unresponsive to labor market conditions.

27

C

Skill-biased technical change and the decline in employment

A …nal related explanation of the secular decline in male employment rates does not appeal to the productivity slowdown, but rather to the concurrent rise in wage inequality in the 1970s and 1980s. Low-skilled workers in the United States experienced sustained declines in their real wages over this period (Bound and Johnson, 1992; Juhn, Murphy and Topel, 1991, 2002), a fact reiterated in Figure 2. This fact in turn suggests a simple explanation for the decline in low-skilled employment: If marginal workers face reductions in their wage, it seems intuitive that they would respond by withdrawing their labor supply (Juhn, 1992). Our analysis provides a number of interesting perspectives on this hypothesis. First, it is worth re-emphasizing that, since our model explains just part of the overall rise in trend nonemployment, other explanations play a complementary role. Consider the timing of the rise in nonwork predicted by our model compared to the timing of the rise in wage inequality. The decline in wages experienced by low-skilled workers starting in the 1970s halted by the early 1990s, and reversed signi…cantly later that decade (Juhn, Murphy and Topel, 2002). In contrast, our simulations in Section IV reveal that, while the model could account for the persistence of the rise in nonemployment into the late 1990s and 2000s, it under predicts the medium-term rise in the 1980s. Thus, there is room for a joint explanation of the overall decline in trend employment rates. In addition to this, however, our model further highlights an important necessary condition for declines in the level of wages— such as those associated with the rise in wage inequality— to have an impact on employment rates: It must be that the payo¤ from nonwork (denoted b in our model) did not fall in tandem with the wages of less-skilled workers. Prior literature often has assumed that it would, usually by appealing to the fact that unemployment compensation is often a …xed fraction of prior wages. To the extent that this were so, reductions in wage levels of low-skilled workers that accompanied the rise in wage inequality would have a muted e¤ect on employment. Assessing the extent to which replacement rates have risen over time, especially among the low-skilled, is therefore a worthy topic of future research.

VI

Conclusion

Rates of joblessness among males in the United States have risen dramatically since the 1970s. These trends are particularly acute among the low-skilled. This paper provides an economic rationale through which changes in wage growth— both aggregate wage growth across time, and wage growth associated with the accumulation of work experience— may have an e¤ect

28

on work incentives. In particular, the paper shows that in a generic model of labor supply, the interaction between a positive return to experience and the trend growth in wages driven by productivity will cause a decrease in the rate of productivity growth to increase equilibrium nonemployment. Accordingly, our modeling provides a novel explanation for correlation between the growth rate and the employment rates, a correlation that is di¢ cult to derive in traditional models with steady states. The paper examines both types of wage growth— the overall trend in real wages and the return to experience. It con…rms the well-known …nding that wage growth has fallen since the 1970s, especially for low-skilled workers. It presents novel evidence that the return to experience has also fallen sharply for the lowest-skilled workers. In contrast, as the previous literature has emphasized and as we con…rm, for most workers the return to experience has increased. The paper combines the evidence on wage growth and the returns to experience with its model of labor supply to show that much of the increase in nonemployment among lowskilled males in the United States since 1970, and around half of the increase in aggregate male nonemployment can be explained by the model. Thus, this paper introduces both a new explanation for the longstanding puzzle that productivity growth rates and employment rates move together, and provides evidence that this explanation has signi…cant empirical relevance. A number of important issues arise for future work in the light of these results. First, in an economy such as the United States with limited social insurance mechanisms, it is natural to ask what sources of income individuals have at their disposal when they experience persistent periods out of work. Potential sources may include income from intermittent employment spells with limited scope for human capital accumulation, and income of other household members (which may interact with increases in female labor market participation over time). Future study of these alternative income sources would shed important light on why employment rates among the low-skilled have been so elastic over time. Second, what caused the equilibrium deterioration in wage growth we see in the data? Of particular interest is why the experience-earnings pro…les among male high school dropouts ‡attened since the 1970s. Our analysis suggests this is unlikely to be related to increased di¤erences between potential and actual experience, sources of selection over time, or to particular data sources. Further analysis of the determinants of the returns to experience seems warranted to provide a coherent explanation for these trends.

Notes: Data are taken from March Current Population Survey microdata for white males aged 16 to 64 with fewer than 30 years of potential experience, who report that they are neither students nor self employed. Nonemployment and nonparticipation rates are respectively computed as the fraction of year spent out of work and out of the labor force. Weeks worked prior to 1976 are intervalled. Rates prior to 1976 are computed by applying within-interval means from post-1976 data to pre-1976 data. Bold black lines are HP trends with an annual smoothing parameter of 100.

Figure 2. Trend Hourly Wage Growth by Education 4 3

1

2010

2005

2000

1995

1990

1985

1980

1975

1970

0 1965

Real Wage Growth (Percent)

2

-1 -2 -3 -4 Productivity Growth

9-11 years

12 years

13-15 years

16+ years

Notes: Authors’ calculations based on March Current Population Survey microdata from 1968 to 2006. The series report HP filtered real annual wage growth by education group. Data are for white males aged 16 to 64 with fewer than 30 years of labor market experience. Hourly wages are computed by dividing weekly wages by weekly hours. Aggregate wages are computed as the mean of the distribution of hourly wages, reweighted to hold constant the distribution of experience using the method of DiNardo, Fortin and Lemieux (1996). Productivity growth is computed from the BLS output per hour series for the business sector. The HP smoothing parameter is 100.

Figure 3. Experience-Earnings Profiles, by Education and Census Year A. 9-11 Years of Education

1.75

1.75

1.5

1.5

1.25 1 0.75 0.5

1.25 1 0.75 0.5

0.25

1960

1970

1980

1990

2000

2001-07

0.25

0

1960

1970

1980

1990

2000

2001-07

0 0

10

20 Potential Experience, Years

30

0

C. 13-15 Years of Education

2 1.75

1.75

1.5

1.5

1.25 1 0.75 0.5

10

20 Potential Experience, Years

30

D. 16+ Years of Education

2

Log Earnings, Normalized

Log Earnings, Normalized

B. 12 Years of Education

2

Log Earnings, Normalized

Log Earnings, Normalized

2

1.25 1 0.75 0.5

0.25

1960

1970

1980

1990

2000

2001-07

0.25

0

1960

1970

1980

1990

2000

2001-07

0 0

10

20 Potential Experience, Years

30

0

10

20 Potential Experience, Years

30

Notes: Profiles are based on data for full-time, full-year white males aged 16 to 64 from the 1960 to 2000 decennial Censuses, and pooled 2001 to 2007 American Community Survey samples. Mean log earnings are normalized by the mean log earnings of workers entering the labor market.

Figure 4. Capitalized Value of Experience-Earnings Profile, Normalized to 1970, 9-11 Years of Education, by Census Year and Discount Rate

Capitalized Value of Earnings, Normalized to 1970

120

100

80

60

40

20 r = 0.033

r = 0.04

r = 0.06

r = 0.08

0 1960

1970

1980

1990

2000

2010

Census Year

Notes: Authors’ calculations of the capitalized value of earnings over a thirty year horizon, discounted at rate r, and normalized to equal 100 in 1970. Data used for the calculation are the experience profiles for 9–11 years of education underlying Figure 3A.

Notes: Profiles are based on same data as those underlying Figure 3. Mean log earnings are normalized by the mean log earnings of workers entering the labor market. Data points for 2010 are imputed under the assumption that the experience-earnings profile from pooled 2001 to 2007 ACS data is time invariant.

Notes: Authors’ calculations based on general model of Section IV. Figure plots the response to a permanent unanticipated decline in gw from 3 percent to –3 percent. The discount rate r = 0.04, and the experience-earnings profile is fixed at its 1980 level in Figure 3A.

Figure 7. Model Response of Nonemployment among High School Dropouts

A. Simulation: Unanticipated Shocks

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0 1965

1970

Varying both g_x and g_w

Varying g_w only

Varying g_x only

Trend Nonemployment (data)

1975

1980

1985

1990

1995

2000

2005

2010

B. Simulation: Anticipated Shocks

0.35

0.3

0.25

0.2

0.15

0.1

0.05

Varying both g_x and g_w

Varying g_w only

Varying g_x only

Trend Nonemployment (data)

0 1965

1970

1975

1980

1985

1990

1995

2000

Notes: Authors’ calculations based on general model of Section IV. Unanticipated shocks: Cross sectional experience profiles (Figure 3A) and aggregate wage growth (Figure 2) are fed through as unanticipated shocks. Anticipated shocks: Cohort experience profiles (Figure 5A) and aggregate wage growth (Figure 2) are fed through the model as anticipated shocks. The discount rate r = 0.04. Simulations that vary gw only (squares) hold the experience profile fixed at its 1980 level. Simulations that vary gx only (pluses) hold aggregate wage growth fixed at the temporal mean of the series for high school dropouts in Figure 2 (approximately zero).

Notes: Authors’ calculations based on general model of Section IV. Observed changes in the experience-earnings profile and aggregate wage growth are fed through the model as unanticipated shocks (as in Figure 7A). The discount rate r = 0.04. When the experience-earnings profile is fixed, it is held at its 1980 level. When aggregate wage growth is fixed, it is held at zero.

Figure 9. Implied Response of Nonparticipation by Education to Observed Changes in Experience-Earnings Profile and Aggregate Wage Growth A. 9-11 Years of Education

B. 12 Years of Education

0.35

0.35

0.3

0.3

0.25

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05

0 1965

1970

1975

1980

1985

1990

1995

2000

2005

2010

0 1965

1970

1975

1990

1995

2000

Varying both g_x and g_w

Varying g_w only

Varying g_x only

Trend Nonparticipation (data)

Varying g_x only

Trend Nonparticipation (data)

C. 13-15 Years of Education 0.3

0.3

0.25

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05

1975

1980

1985

1990

1995

2005

2010

2005

2010

D. 16+ Years of Education 0.35

1970

1985

Varying g_w only

0.35

0 1965

1980

Varying both g_x and g_w

2000

2005

2010

0 1965

1970

1975

1980

1985

1990

1995

2000

Varying both g_x and g_w

Varying g_w only

Varying both g_x and g_w

Varying g_w only

Varying g_x only

Trend Nonparticipation (data)

Varying g_x only

Trend Nonparticipation (data)

Notes: Authors’ calculations based on general model of Section IV. Observed changes in the experience-earnings profile and aggregate wage growth are fed through the model as unanticipated shocks (as in Figure 7A). The discount rate r = 0.04. When the experience-earnings profile is fixed, it is held at its 1980 level. When aggregate wage growth is fixed, it is held at zero.

VIII A

Appendix

Main Theoretical Results

Derivation of Equation (1) Imagine …rms face a constant returns to scale production technology that uses e¢ ciency units of labor A (x; t) n, as well as capital k to produce output y according to y = F (A (x; t) n; k) , where A (x; t) egw t+gx x : (1) From the linear homogeneity of the production technology, the marginal products are homogeneous of degree zero, so that we can write n Fj (A (x; t) n; k) = Fj A (x; t) ; 1 k

It follows that, when the individual is just indi¤erent between working or not, the time derivative of the di¤erence between the wage and the reservation wage is given by (w_

w_ R )jw=wR = (r

gw ) (t) :

(5)

Under the assumptions that r gw > 0 and wx (x ( ) ; ) > 0 for all , the shadow value of experience in equation (12) has the property that (t)

> 0 if h ( ) = 1 for any > t; = 0 if h ( ) = 0 for all > t:

(6)

Given this, we can conclude that (w_

w_ R )jw=wR

> 0 if h ( ) = 1 for any > t; = 0 if h ( ) = 0 for all > t:

(7)

Thus, whenever a worker is indi¤erent between working or not at a point in time, two outcomes are possible: If he intends to work at any point in the future, he will start working

1

now and will work for the rest of his life, since his o¤ered market wage is rising above his reservation wage from below. On the other hand, if he never intends to work in the future, he will be indi¤erent between working and not working for the rest of his life. It follows that any wage o¤er slightly above the reservation wage will lead a worker to work for the rest of his life, and any o¤er slightly below his reservation wage will lead a worker to not work for the rest of his life.

Solving for the reservation wage yields equation (9) in the main text. Finite Lifetimes and Nonlinear Returns to Experience In the presence of labor market frictions, the expression for the marginal value of experience (analogous to equation (12) in the main text) for an individual who enters the labor market is given by ~=E

Z

T

e

r

I ( ) wx (x ( ) ; ) d ;

(11)

0

where I ( ) is an indicator function that equals one if the individual is employed at time and zero otherwise, and where we have used the results of Proposition 1, which apply analogously to this more elaborate problem. Expanding and collecting the relevant terms 2

In general, solving this expression further is complicated by the presence of the terms in I ( ) and x ( ), which are (related) random variables. However, it is possible to get a sense of its likely form by noting that the job-…nding rate f is very large in practice. For example, estimates reported in Fujita and Ramey (2006) suggest that f 4 on an annual basis over the period 1976 to 2006. This observation has a number of useful implications in the present context: 1. The probability of employment E [I ( )] p ( ) evolves according to the di¤erential 0 equation p ( ) = f [1 p ( )] sp ( ). Together with the initial condition p (0) = 0, f . For large f , a very good approximation to this implies that p ( ) = 1 e (s+f ) s+f f the latter is p ( ) s+f p. 2. The variance of an individual’s employment status var [I ( )] = p ( ) [1 p ( )] f p (1 p) for large f . In addition, since p s+f 1, it follows that var [I ( )] 0. R 3. Finally, note that an individual’s experience x ( ) = 0 I ( ) d . It follows from the above that E [x ( )] p and var [x ( )] 0. Given these approximations, it is possible to write Z T Rp ~ w (0; 0) e (r gw ) + 0 gx (z)dz pgx (p ) d :

(13)

0

Solving for the reservation wage of an individual entering the labor market yields wR (0; 0)

~ b (0) , where ~ = 1 +

Z

0

T

e

(r gw ) +

Rp 0

1 gx (z)dz

pgx (p ) d

:

(14)

Comparison of the latter with equation (15) in the main text reiterates the message of Section II.C. The approximate e¤ect of allowing for labor market frictions is to attenuate slightly f 1. the return to experience by a factor equal to p s+f

C

Changes in the Experience-Earnings Pro…le: Robustness

Potential vs. Actual Experience A potential confound to the evidence presented in Figure 3 is that we observe only potential, not actual experience in the data. A particular cause for concern is that declines in employment rates among high school dropouts in Figure 1 have led to a widening of the gap between potential and actual experience among this group of workers. Consequently, it is possible that this form of reverse causality could account for some of the ‡attening of the observed relationship between mean log earnings and potential experience in Figure 3, as older workers with high potential experience increasingly accumulate fewer years of actual experience, and thereby earn less. 3

We perform a simple exercise that we believe provides an upper bound on the magnitude of this e¤ect. Imagine, counterfactually, that employment is i.i.d. across workers at any given point in time. In steady state, this will imply that the actual experience of a worker is equal to the employment rate multiplied by potential experience. It follows that, in this environment, accounting for the di¤erence between potential and actual experience amounts simply to a rescaling of the horizontal axis in Figure 3A, by a proportion equal to the employment rate. This exercise provides an upper bound for the magnitude of these e¤ects because employment is not i.i.d. across workers, but is rather persistent. In particular, by focusing on full-time, full-year workers we are considering workers who are more than averagely attached to the labor market. Appendix Figure 1 presents the results of this exercise. It illustrates the potential experience–earnings pro…les from Figure 3 for 1970 and 2000, as well as the implied actual experience–earnings pro…les that would obtain by rescaling the horizontal axis by the trend employment rates in 1970 and 2000 respectively.1 Appendix Figure 1 shows that, although some of the ‡attening of the experience–earnings pro…le can be accounted for by a widening gap between potential and actual experience, the magnitude of these e¤ects is likely to be small. Even after accounting for an upper bound on these e¤ects, after …ve to ten years of experience earnings remain around 45 log points lower in 2000 compared to 1970. In addition to this, we also use data from the core sample of the Panel Study of Income Dynamics to explore this possibility further. The sample restrictions imposed mirror those used in the Census samples described in the main text. We focus on full time full year white male household heads aged 16 to 64 with 9 to 11 years of completed schooling. Potential experience is constructed as age minus years of completed schooling minus six.2 Actual experience is constructed as follows. In the …rst year a respondent is observed, the actual experience calendar is intialized using data on the number of years worked since age 18.3 Actual experience is then updated in each consecutive survey by adding the fraction of weeks worked in the survey year to the cumulative value of actual experience in prior years. Appendix Figure 2 presents the results of this exercise for PSID data pertaining to the years 1967 to 1996.4 It plots measures of average actual experience against potential experience from the method described above. Years of data are pooled into three groups to obtain larger sample sizes. The results suggest that there has indeed been a divergence between potential and actual experience in the later years of the sample, consistent with the fact that employment rates have fallen among high school dropouts. However, the magnitudes of these e¤ects are somewhat smaller than those assumed in Appendix Figure 1

The trend employment rates used are 10 percent and 25 percent for 1970 and 2000 respectively (see Figure 1). More complicated corrections that account for time variation in employment rates that workers of di¤erent levels of potential experience have faced in their working lives yield very similar pictures. 2 Years of completed schooling are available only in intervals for the years 1969 to 1974 inclusive. For those years, years of schooling equal are set equal to the value reported in 1968, if it is observed and is consistent with the intervalled variable in subsequent surveys. Otherwise, we assign the midpoint value of the intervalled data. 3 Data on the number of years worked since age 18 is unavailable prior to 1974. Consequently, respondents who worked only prior to 1974 were excluded. For respondents who worked before and after 1974, the number of years worked is backcasted using information in the pre-1974 surveys on whether the respondent worked. 4 The switch to a biennial survey in 1997 complicates the construction of the actual experience variable, since it does not contain data on employment in the year prior to the survey year.

4

1. There it was assumed that the ratio of actual to potential experience was equal to 0.9 in 1970, and 0.75 in 2000, the respective trend employment rates in those two periods. The results in Appendix Figure 2 suggest that the ratio dropped from 0.9 to 0.8, suggesting that the exercise underlying Appendix Figure 1 is indeed an upper bound. Selection Additional potential confounds relate to forms of selection that vary over time. We highlight two of these possibilities here. First, since the fraction of each cohort of workers that are high school dropouts has fallen over time, it is natural to conjecture that dropouts have become increasingly lower skilled over time. An implication would be that, at any given point in time, measured experience–earnings pro…les among dropouts would overstate the return to experience, since older dropouts are of higher quality than their younger counterparts for a reason unrelated to their accumulation of experience. Thus, selection of this sort could lead to a spurious ‡attening of the experience pro…le if the dropout rate were to fall over time at a decreasing rate. Recent research suggests that this is unlikely to be a concern over the sample period. In fact, the notion that high school dropouts have become increasingly lower skilled over time receives little support in careful analyses of graduation rates in the U.S. Heckman and LaFontaine (2007) demonstrate that most of the decline in headline dropout rates among white males (e.g. from the National Center of Education Statistics) can be attributed to increases in the fraction of GED recipients in successive cohorts. In addition, Heckman and Rubinstein (2001) and Heckman and LaFontaine (2006) argue that, while such GED recipients exhibit similar cognitive ability to high school graduates, their labor market outcomes mirror those of high school dropouts. This suggests that compositional changes related to increased take up of the GED are unlikely to explain our results for dropouts.5 A second potential form of selection can arise if there are heterogeneous returns to experience across workers. In such an environment, one would expect individuals with high returns to labor market experience to be more likely to choose to work. Since the experience– earnings pro…les in Figure 3 depict the average returns to experience among those that choose to work, it is likely that they overstate the average return to experience among the entire working and non–working population. This source of selection also may vary over time. As employment rates fall among high school dropouts, the measured return to experience that we observe will report the average returns for an increasingly select group of workers. Consequently, we would anticipate this form of selection to lead us to observe a steepening of experience–earnings pro…les, as the only workers who choose to work will be those with increasingly higher returns to experience. Comparison with Previous Literature A number of studies in the literature on wage inequality has estimated the “experience premium,”measured as the log wage gap between experienced workers (typically with 25 years of experience) and less experienced workers (5 years of experience) using CPS data (see, for example, Katz and Autor, 1999; Weinberg, 5

Although high school dropouts are our main focus, it is worth noting that the grouping of individuals with a GED quali…cation with high school graduates may lead to some spurious steepening of the measured experience–earnings pro…le for high school graduates. This would tend to work against our ability to account for increases in nonemployment among high school graduates.

5

2005; Autor, Katz and Kearney, 2008). These studies all have documented evidence for a rise in the experience premium among high school graduates and college graduates over time. We con…rm that these …ndings are consistent with our estimates from Census and ACS data. Appendix Figure 3 addresses this question by plotting the experience premium by education group across time using the Census/ACS underlying Figure 3, as well as for comparable CPS samples. The picture painted in Appendix Figure 3 is a relatively reassuring one: Despite some di¤erences in the measured levels of the experience premium in the two di¤erent sources of data, the trends in the experience premium by skill are consistent over time.6 As reported in the above–cited studies, the experience premium among high school and college graduates has trended upward over time in both the CPS and Census/ACS samples we use. However, consistent with the impression in Figure 3A that the experience–earnings pro…le for dropouts has ‡attened over time, the experience premium among high school dropouts has trended downward since 1970 in both data sources. Thus, our empirical work con…rms earlier …ndings in the literature that the return to experience for workers who have at least a high school education have enjoyed an increase in the return to experience. Our work has the new and important …nding, however, that the workers with the lowest educational attainment have faced a decrease in the returns to experience.7

6

While the 25/5 experience premium is a commonly used measure, the high frequency movements observed in the CPS estimates should be treated with caution due to the low sample sizes available in the CPS. The standard errors around each datapoint in Figure 6 averaged 0.16 for dropouts, 0.09 for high school graduates, 0.12 for some college, and 0.14 for college graduates. 7 An additional useful implication of this …nding is that it is also consistent with evidence reported in Lemieux (2006, Figure 1) that, aggregated across all education groups, the experience–earnings pro…le has been quite stable since the early to mid 1970s. The simple reason is that increased returns to experience among higher skilled workers have been o¤set by the declines in returns to experience that we document for high school dropouts.

6

Appendix Figure 1. Potential vs. Actual Experience and Changes in Experience-Earnings Profiles among High School Dropouts

9-11 Years of Education

2 1.75

Log Earnings, Normalized

1.5 1.25 1 0.75 0.5

0.25

1970 (potential)

2000 (potential)

1970 (imputed actual)

2000 (imputed actual)

0 0

10 20 Potential /Actual Experience, Years

30

Notes: Non-dashed lines are cross-sectional potential experience-earnings profiles among fulltime, full-year white males aged 16 to 64 from the 1970 and 2000 decennial Censuses replicated from Figure 3A. Dashed lines represent actual experience-earnings profiles that would be observed under steady state employment rates of 90 percent in 1970 and 75 percent in 2000, assuming that employment is i.i.d. across workers.

Notes: Measures of average actual experience against potential experience for pooled years from the Panel Study of Income Dynamics. Non-dashed straight lines represent least squares regressions with the intercept constrained to equal zero. For details on the construction of the measures of actual and potential experience, see Appendix B.

Notes: The 25/5 experience premium is defined as the difference in mean log earnings among workers with 25 vs. 5 years of experience among full-time, full-year white males aged 16 to 64. Data are taken from the decennial Censuses from 1960 to 2000, pooled 2001 to 2007 American Community Surveys, and March Current Population Survey microdata. The black bold lines plot linear time trends of CPS data.

Why Does Trend Growth AFFect Equilibrium ...

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